The 2 1/2-D Sketch
First, it must be understood that the number 2 1/2 is not to be taken literally. Marr's 2 1/2-D sketch has nothing to do with actual half dimensions nor with fractals which have fractional dimensions. Rather, this number represents the concept that in reality, we do not see all of our surroundings.
Marr claims that we do not actually see all three dimensions surrounding us. Rather, we construct the three dimensions in our mind and project them onto the objects surrounding us. To illustrate, consider someone with her back turned to you. You can only see half of her body. Though what you do see has, within itself, three dimensional relationships which you can perceive. However, you only assume you know what the front half of her looks like, you can't actually see it. If she were to turn towards you and have no facial features, you would be, at the least, shocked.
The point of Marr's 2 1/2-D sketch is that we must remember that what we see is, by its very nature, viewer-centered. We only actually see things as they relate to us. We cannot see things either as related to others' perspectives or in an objective standpoint as they relate only to themselves. More specifically, what we see is a projection of our surroundings onto a 2-dimensional plane, our retinae. The key to perceiving three dimensions is that we have two retinae. The angles at which our eyes must point to focus on an object determines how far away an object appears to us.
A good way to understand this concept is to imagine a stereogram as reality. Our eyes actually cannot tell the difference between the two, hence the illusion that we are viewing a 3-D model when we are looking at the 2-D page. The page can be looked at as being the projection of reality onto a plane. However, in order to focus on the objects within the planes, we must direct our eyes at different angles, creating the illusion of depth on a flat page.
The 2 1/2-D sketch is important in many areas of vision study, as it emphasizes that we are not actually aware of all are surroundings and so construct details to fill in the gaps. Furthermore, it carries implications forthe way in which our mind operates.
Mike Akins '99
May 25, 1996.